QCD Symmetries in eta and etaprime mesic nuclei Steven Bass Chiral - PowerPoint PPT Presentation

QCD Symmetries in eta and etaprime mesic nuclei Steven Bass Chiral symmetry, eta and eta´ physics: the masses of these mesons are 300-400 MeV too big for them to be pure Goldstone bosons  Famous axial U(1) problem of QCD Additional mass is associated with non-perturbative gluon dynamics Recent developments in eta´ physics: the eta´ in nuclear matter and odd l-wave exotics from CERN  How should the eta and eta-prime masses be modified in nuclei ?  Possible bound states and eta(-prime) nucleon scattering lengths Vienna, September 19 2014 1

From Quarks to Hadrons • Confinement • Dynamical chiral symmetry breaking: » Chiral condensate, pions, kaons, ... Goldstone bosons • Axial U(1) Symmetry breaking ... Big masses for eta and etaprime • Using nuclei to probe symmetries and possible restoration (both quark and gluonic effects) 2

Chiral symmetry • QCD Lagrangian with massless quarks exhibits chiral symmetry • Noether currents • No parity doublets in hadron spectrum  Spontaneous Chiral symmetry breaking: non zero condensate spontaneously breaks the symmetry  Nonet of near massless Goldstone bosons with J P = 0 - • Identify with pion, kaon, eta with meson mass squared proportional to m q … where is the singlet boson ? 3

Eta and Etaprime masses • Mass matrix • Diagonalize • Eigenvalues • With no glue: chiral symmetry „predicts“ eigenstates with masses 300 MeV „too small“ » „eta“ degenerate with the pion » „etaprime“ with mass 4

Chirality and anomalous glue • Perturbative QCD conserves chirality for massless quarks • Confinement and vacuum tunneling processes (instantons, …) connect left and right handed quarks 5

Confinement and chiral symmetry • Scalar confinement dynamically breaks chiral symmetry – E.g. In Bag model confinement the Bag wall connects left and right handed quarks – Quark – pion coupling and the pion cloud of the nucleon • Pions, kaons, eta ... as Goldstone bosons • OGE as residual vector (colour hyperfine) interaction 6

Axial U(1) symmetry • Extra gluonic mass term is associated with the QCD axial anomaly • plus gluon topology (note the difference with „perturbative glue“) • ´ t Hooft, Veneziano, Witten, Crewther, … – possible connection to confinement (Kogut and Susskind) Can we observe physical manifestation of this anomalous glue in low-energy physical processes involving eta and eta´mesons ? 7

Glue in etaprime physics • Glue enters through the anomaly equation … • Three important places it can contribute » Gluonic potential associated with QCD vacuum gives the etaprime a big mass » The etaprime has a large singlet component  coupling to gluonic intermediate states (OZI violation) » Gluonic Fock components in the etaprime wavefunction 8

U(1) extended chiral Lagrangian • Low energy effective Lagrangian – constructed to reproduce the axial anomaly in the anomalous divergence equation and the gluonic mass term for the singlet boson • Q is the topological charge density and the gluonic potential yields the gluonic contribution to the etaprime mass term • Couple to sigma mean field and repeat … 9

New Compass results • Iterate in Bethe Salpeter equation dynamicaly generates 1 -+ exotic resonance with mass ~ 1400 MeV [SDB and E Marco, PRD 65 (2002) 057503] Compass, hep-ex 1408.4286 10

Eta(prime) bound states in nuclei [SDB + AW Thomas, Phys Lett B634 (2006) 368, Acta Phys Pol B 45 (2014) 627] • New experiments + big effort ... • Binding energies and effective masses in nuclei are sensitive to – Coupling to scalar sigma field in the nuclei in mean field approx. – Nucleon-nucleon and nucleon-hole excitations in the medium • TH: Solve for the meson self-energy in the medium – Where a is the „eta(prime) - nucleon scattering length“ 11

Eta bound-states in nuclei • Sigma mean field couples to light quarks and not to strange quarks  Flavour-singlet component is important ! The bigger the eta-eta´mixing angle, the bigger the singlet component in the eta  greater the attraction  more binding  bigger eta-N scattering length Likewise, more mixing gives smaller singlet component in the eta‘  reduced binding and smaller eta‘N scattering length Without QCD axial anomaly, eta‘ a strange state and no mass shift QCD arguments  gluonic mass term is suppressed in the medium but theory technology to calculate the size of the effect direct from QCD still some time away  look at QCD inspired models 12

QCD and models • Include key aspects of QCD as input motivation » Confinement » Chiral symmetry » Eta-etaprime mixing • Quark-meson coupling, chiral coupled channels, NJL, linear sigma model... include different aspects of QCD input with very different predictions • Suppose we see a bound state or mass shift  » What do we learn about QCD ? 13

QCD Inspired Models • Quark Meson Coupling Model: – Can vary the mixing angle ! – Use large eta and eta´masses to treat the eta and eta´as MIT Bags embedded in the medium with coupling between the light-quarks and the sigma mean field Solve for in-medium mass and binding energy  Extract an „effective“ scattering length for the model  Increases with increasing singlet component in the eta ! • Hints from CBELSA/TAPS for etaprime [Nanova et al, 2013] 14

COSY 11 • E. Czerwinski et al (2014), COSY 11 Collaboration, Phys. Rev. Lett. 113 (2014) 062004 15

Eta-etaprime mixing and mass shift • Phenomenology and EP data » On-shell Re[a_eta] ~ 0.9 fm [Green + Wycech, Arndt et al] » COSY-11 ~ 0.7 fm from FSI in pp  pp eta » COSY-11 a_eta‘ new [previous slide] • Chiral coupled channels treating the eta as a pure octet state » Small mass shift and small Re[a_eta] ~ 0.2 fm » For etaprime: including axial U(1) degrees of freedom gives considerable expansion in number of potentials • N*(1535) – 3 quark state (1s)2(1p) in Quark model and lattice calculations or K-Sigma quasi-bound state from Chiral coupled channels in octet approx. – In data and in both QMC and chiral coupled channels models, negligible shift in excitation energy in nuclei 16

Comparison with NJL • NJL model using density dependent instanton interaction – QCD input: chiral symmetry, no confinement, medium a Fermi gas of quarks instead of nucleons, mass shift for the eta´up to ~ 150 MeV » Phys Rev C74 (2006) 045203 • Suppose eta-eta´ mass splitting comes just from anomaly, proportional to quark condensate  80-100 MeV mass shift » Phys Rev C85 (2012) 032201, Phys. Rev. C88 (2013) 064906 17

Outlook and Conclusions • Eta and etaprime physics probes the role of long range gluonic dynamics • Etas and etaprimes in nuclei: – Aspects of Confinement, chiral symmetry and their interplay, range of masses for pseudoscalars to be treated as Goldstone states in the models – Binding energies and scattering lengths sensitive to the flavour- singlet component in the eta and eta´ – Without QCD anomaly, no effect in the eta´ – QMC model: » Factor of 2 increase in the eta-nucleon scattering length and binding energy in nuclei with eta-etaprime mixing cf. Theory prediction with a pure octet eta » Good agreement with CBELSA/TAPS for the eta´ ... Awaits experimental input! ... ELSA (BOG-OD), GSI (etaprime), COSY (eta). 18

CBELSA/TAPS: Transparency Ratios • Medium is reasonably transparent to eta´propagation 19

Theoretical development 20

For extra reading 21